Sample Size Determination for the Bayesian t-test and Welch’s test Using the Approximate Adjusted Fractional Bayes Factor

When two independent means $\mu_1$ and $\mu_2$ are compared, $H_0: \mu_1=\mu_2$, $H_1: \mu_1\ne\mu_2$, and $H_2: \mu_1>\mu_2$ are the hypotheses of interest. This paper introduces the \texttt{R} package \texttt{SSDbain}, which can be used to determine the sample size needed to evaluate these hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) implemented in the \texttt{R} package \texttt{bain}. Both the Bayesian t-test and the Bayesian Welch's test are available in this \texttt{R} package. The sample size required will be calculated such that the probability that the Bayes factor is larger than a threshold value is at least $\eta$ if either the null or alternative hypothesis is true. Using the \texttt{R} package \texttt{SSDbain} and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments.